Towards nonuniform distributions of unisolvent weights for high-order Whitney edge elements - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Calcolo Year : 2022

Towards nonuniform distributions of unisolvent weights for high-order Whitney edge elements

Abstract

We propose to extend results on the interpolation theory for scalar functions to the case of differential k-forms. More precisely, we consider the interpolation of fields in the finite element spaces of trimmed polynomial k-forms of arbitrary degree r ≥ 1, from their weights, namely their integrals on k-chains. These integrals have a clear physical interpretation, such as circulations along curves, fluxes across surfaces, densities in volumes, depending on the value of k. In this work, for k = 1, we rely on the flexibility of the weights with respect to their geometrical support, to study different sets of 1-chains in T for a high order interpolation of differential 1-forms, constructed starting from “good” sets of nodes for a high order multi-variate polynomial representation of scalar fields, namely 0-forms. We analyse the growth of the generalized Lebesgue constant with the degree r and preliminary numerical results for edge elements support the nonuniform choice, in agreement with the well-known nodal case.
Fichier principal
Vignette du fichier
Nonunif_last_ABR_hal.pdf (632.29 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03114568 , version 1 (19-01-2021)
hal-03114568 , version 2 (12-06-2021)
hal-03114568 , version 3 (30-11-2021)
hal-03114568 , version 4 (22-05-2022)

Identifiers

  • HAL Id : hal-03114568 , version 4

Cite

Ana Alonso Rodríguez, Ludovico Bruni Bruno, Francesca Rapetti. Towards nonuniform distributions of unisolvent weights for high-order Whitney edge elements. Calcolo, 2022, 59 (37). ⟨hal-03114568v4⟩
1376 View
175 Download

Share

Gmail Facebook Twitter LinkedIn More